Abstract
While making decisions we meet different types of uncertainty. Recently the concept of generalized credal set has been proposed for modeling conflict, imprecision and contradiction in information. This concept allows us to generalize the theory of imprecise probabilities giving us possibilities to process information presented by contradictory (incoherent) lower previsions. In this paper we propose a new way of introducing generalized credal sets: we show that any contradictory lower prevision can be represented as a convex sum of non-contradictory and fully contradictory lower previsions. In this way we can introduce generalized credal sets and apply them to decision problems. Decision making is based on decision rules in the theory of imprecise probabilities and the contradiction-imprecision transformation that looks like incoherence correction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Augustin, T., Coolen, F.P.A., de Cooman, G., Troffaes, M.C.M. (eds.): Introduction to Imprecise Probabilities. Wiley, New York (2014)
Bronevich, A.G., Klir, G.J.: Measures of uncertainty for imprecise probabilities: an axiomatic approach. Int. J. Approx. Reason. 51, 365–390 (2010)
Bronevich, A.G., Rozenberg, I.N.: The generalization of the the conjunctive rule for aggregating contradictory sources of information based on generalized credal sets. In: Augustin, T., Doria, S., Miranda, E., Quaeghebeur, E. (eds.) Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications, pp. 67–76. Aracne Editrice, Rome (2015)
Bronevich, A.G., Rozenberg, I.N.: The extension of imprecise probabilities based on generalized credal sets. In: Ferraro, M.B., Giordani, P., Vantaggi, B., Gagolewski, M., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Advances in Intelligent Systems and Computing. 456, pp. 87–94. Springer Verlag, Berlin (2017)
Brozzi, A., Capotorti, A., Vantaggi, B.: Incoherence correction strategies in statistical matching. Int. J. Approx. Reason. 53, 1124–1136 (2012)
Klir, G.J.: Uncertainty and Information: Foundations of Generalized Information Theory. Wiley-Interscience, Hoboken (2006)
Quaeghebeur, E.: Characterizing coherence, correcting incoherence. Int. J. Approx. Reason. 56(Part B), 208–233 (2015)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Bronevich, A.G., Rozenberg, I.N. (2017). Incoherence Correction and Decision Making Based on Generalized Credal Sets. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-61581-3_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61580-6
Online ISBN: 978-3-319-61581-3
eBook Packages: Computer ScienceComputer Science (R0)